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Documentation on comp_linearmap #21333

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BoltonBailey opened this issue Feb 1, 2025 · 0 comments
Open

Documentation on comp_linearmap #21333

BoltonBailey opened this issue Feb 1, 2025 · 0 comments
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documentation Improvements or additions to documentation good first issue Good for newcomers help-wanted The author needs attention to resolve issues

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@BoltonBailey
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BoltonBailey commented Feb 1, 2025

Just a quick issue as a reminder since I'm in the middle of something, but this docstring (and below) seems wrong: f is not the linear one, g is

/-- If `g` is convex on `s`, so is `(f ∘ g)` on `f ⁻¹' s` for a linear `f`. -/
theorem ConvexOn.comp_linearMap {f : F → β} {s : Set F} (hf : ConvexOn 𝕜 s f) (g : E →ₗ[𝕜] F) :
ConvexOn 𝕜 (g ⁻¹' s) (f ∘ g) :=
⟨hf.1.linear_preimage _, fun x hx y hy a b ha hb hab =>
calc
f (g (a • x + b • y)) = f (a • g x + b • g y) := by rw [g.map_add, g.map_smul, g.map_smul]
_ ≤ a • f (g x) + b • f (g y) := hf.2 hx hy ha hb hab⟩

@BoltonBailey BoltonBailey added good first issue Good for newcomers help-wanted The author needs attention to resolve issues documentation Improvements or additions to documentation labels Feb 1, 2025
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